In fig. REF  we show the variation of our statistics with \(T_{vir}\)  at different fixed values of \(\zeta \)  and \(R_{mfp}\)  on the left panel and vice versa on the right panel. The top row shows the hole statistics and the bottom row shows connected region statistics. If the value of \(R_{mfp}\)  is fixed then for a given \(\zeta \) , decreasing \(T_{vir}\)  corresponds to an increasing ionized fraction and same holds for a fixed \(T_{vir}\)  and increasing \(\zeta \) . Moreover, if the value of \(\zeta \)  is higher then complete ionization is obtained at a relatively larger value of \(T_{vir}\) , since the effect of increasing \(\zeta \)  is to increase the rate of progress of ionization. Therefore ionization is achieved at a lower collapse fraction (or higher \(T_{vir}\) ) for a higher \(\zeta \) . This is captured in the left panels of the figure. On the other hand if the collapse fraction is high (or low \(T_{vir}\) ) then ionization is acheived at a lower \(\zeta \) . This is captured in the right panels. This variation is captured by the red, green, dark blue and skyblue dotted lines. Thus, at high \(T_{vir}\)  values there are few isolated bubbles, which initially increase as \(T_{vir}\)  decreases. A further decrease in \(T_{vir}\)  will lead to more numerous bubbles and increased mergers which decreases the number of holes. Therefore the number of holes first increases and then decreases (see fig. REF ). In fig. REF , this turnover is seen at \(\zeta =13\)  (shown in red) where the ionization history is varying faster. For other \(\zeta \)  values this turnover happens beyond the range of \(T_{vir}\)  values plotted in fig. REF . The turnover is a result of the competition between the rate of appearance of new collapsed sources and the rate of bubble mergers [1]}. On the other hand, for a fixed \(\zeta \)  (or \(T_{vir}\) ) and vary \(R_{mfp}\) , we find that the variation with \(T_{vir}\)  (or \(\zeta \) ) is almost insensitive at high values of \(T_{vir}\)  (or lower \(\zeta \) ) corresponding to larger values of \(x_{HI}\) . A smaller value of mean horizon of ionizing radiation leads to reionization becoming slower. This trend is captured by purple, orange, yellow and cyan markers. This parameter is known to be sensitive only when ionized region sizes approaches \(\sim R_{mfp}\)  [2]}.
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